According to this answer, students at university in the medieval period were generally paying their own way and were independently rich or were selected by the crown or the church, the latter making up the majority of students.
What academic expectations were there of these students? Did these expectations vary between the different types of students?
Entrance varied dramatically by time and place, with students enrolling at Oxford or Paris around the age of 14 to study the liberal arts, and at Bologna around the age of 30 to study law.
Historically the curriculum of a liberal arts degree was first the study of the trivium of grammar, rhetoric and logic, followed by the quadrivium of arithmetic, geometry, music and astronomy. During the Renaissance the curriculum expanded to include the Aristotelian sciences of physics, metaphysics, and moral philosophy.
All studies were in Latin, though Greek might have been used for the study of Euclid's geometry, and later for the study of the Aristotelian sciences. Note that the initial trivium, taught in Latin, was actually the study of Latin grammar; of Latin rhetoric, and of Latin logic. and thus was the study of first the written language, the spoken language, and then of constructing written and spoken argument in the language.
So far from requiring a solid knowledge of Latin prior to entrance, the first few years of a student's studies were devoted to its mastery: written; spoken; and as a means of analytical thought. Of course to be recognized as a candidate for sponsorship at one of these institutions a young boy would likely be demonstrating aptitude in the language.
For the southern universities modeled on Bologna, studying for an advanced degrees in law, medicine or theology would have as prerequisite prior knowledge of the liberal arts.
Note that the founding of Oxford( teaching 1096, recognized 1167) and Cambridge (1209) precedes the founding of Eton College (1441) by hundreds of years. The concept of a grammar school, where one might begin the study of the first of the liberal arts at a younger age and prior to entering university, post dates the concept of university by centuries.
A person would have to successfully complete what we would now call a "grammar school." Mostly, a person had to be able to read and write, but in several languages. Latin, which was the "universal" language, plus their native language, and many also studied Greek. After the Renaissance, French, Italian, and Spanish. Except for people who were English or German, one of these was probably their native language. They're fairly closely related between themselves, as well as to Latin, making things easier.
Boys coming up through "church" schools also had a thorough grounding in what we would call "religion." Boys pursuing secular studies in "state" schools had more training in history. This may not have been taught as a "separate" course, but part of Latin and Greek texts. (To the extent that they were educated, girls were "home schooled.")
There was very little math and science until the Renaissance and later. Algebra barely existed during the Middle Ages, and Calculus had not been invented. Nor had most of what we know in biology, chemistry, or physics (other than navigation). The main "math" at the time was geometry, which dated back to Euclid, and was often taught as part of some Greek texts, rather than "separately."
